LMFDB - Embedded newform 810.2.i.e.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(109,810)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("810.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			379.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	810.379
Dual form			810.2.i.e.109.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-5.19615 + 3.00000i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.00000i q^{17} +(-1.86603 + 1.23205i) q^{20} +(-1.73205 + 1.00000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -6.00000 q^{26} -2.00000i q^{28} +(4.00000 + 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(2.00000 - 4.00000i) q^{35} +2.00000i q^{37} +(-2.23205 + 0.133975i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(-3.46410 - 2.00000i) q^{43} -2.00000 q^{44} +4.00000 q^{46} +(6.92820 + 4.00000i) q^{47} +(-1.50000 - 2.59808i) q^{49} +(-4.59808 - 1.96410i) q^{50} +(-5.19615 - 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 - 2.00000i) q^{55} +(1.00000 - 1.73205i) q^{56} +(5.00000 + 8.66025i) q^{59} +(-1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-7.39230 - 11.1962i) q^{65} +(-6.92820 + 4.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(3.73205 - 2.46410i) q^{70} +12.0000 q^{71} +4.00000i q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.46410 - 2.00000i) q^{77} +(-2.00000 - 1.00000i) q^{80} -2.00000i q^{82} +(-3.46410 - 2.00000i) q^{83} +(-4.46410 + 0.267949i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.73205 - 1.00000i) q^{88} +10.0000 q^{89} +12.0000 q^{91} +(3.46410 + 2.00000i) q^{92} +(4.00000 + 6.92820i) q^{94} +(6.92820 + 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5	$ 4 q + 2 q^{4} + 4 q^{5} - 4 q^{10} - 4 q^{11} - 4 q^{14} - 2 q^{16} - 4 q^{20} - 6 q^{25} - 24 q^{26} + 16 q^{31} - 4 q^{34} + 8 q^{35} - 2 q^{40} - 4 q^{41} - 8 q^{44} + 16 q^{46} - 6 q^{49} - 8 q^{50} - 16 q^{55} + 4 q^{56} + 20 q^{59} - 4 q^{61} - 4 q^{64} + 12 q^{65} + 8 q^{70} + 48 q^{71} - 4 q^{74} - 8 q^{80} - 4 q^{85} - 8 q^{86} + 40 q^{89} + 48 q^{91} + 16 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 - 4 * q^10 - 4 * q^11 - 4 * q^14 - 2 * q^16 - 4 * q^20 - 6 * q^25 - 24 * q^26 + 16 * q^31 - 4 * q^34 + 8 * q^35 - 2 * q^40 - 4 * q^41 - 8 * q^44 + 16 * q^46 - 6 * q^49 - 8 * q^50 - 16 * q^55 + 4 * q^56 + 20 * q^59 - 4 * q^61 - 4 * q^64 + 12 * q^65 + 8 * q^70 + 48 * q^71 - 4 * q^74 - 8 * q^80 - 4 * q^85 - 8 * q^86 + 40 * q^89 + 48 * q^91 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−1.00000	−	1.73205i	−0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−1.86603	+	1.23205i	−0.417256	+	0.275495i
$21$		0			0
$22$	−1.73205	+	1.00000i	−0.369274	+	0.213201i
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	−0.0932891	−	0.995639i	$-0.529738\pi$
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	0.815604	+	0.578610i	$0.196405\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−6.00000			−1.17670
$27$		0			0
$28$		−	2.00000i		−	0.377964i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	2.00000	−	4.00000i	0.338062	−	0.676123i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$		0			0
$40$	−2.23205	+	0.133975i	−0.352918	+	0.0211832i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	0.212041	−	0.977261i	$-0.431989\pi$
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	−0.740312	+	0.672264i	$0.765322\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	4.00000			0.589768
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.911362	−	0.411606i	$-0.135032\pi$
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.0992202	+	0.995066i	$0.468365\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−4.59808	−	1.96410i	−0.650266	−	0.277766i
$51$		0			0
$52$	−5.19615	−	3.00000i	−0.720577	−	0.416025i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	−4.00000	−	2.00000i	−0.539360	−	0.269680i
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$		0			0
$58$		0			0
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$			8.00000i			1.01600i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.39230	−	11.1962i	−0.916903	−	1.38871i
$66$		0			0
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	−0.859440	−	0.511237i	$-0.829187\pi$
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	0.0130248	+	0.999915i	$0.495854\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$		0			0
$70$	3.73205	−	2.46410i	0.446065	−	0.294516i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$		0			0
$77$	3.46410	−	2.00000i	0.394771	−	0.227921i
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$		0			0
$82$		−	2.00000i		−	0.220863i
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	0.297686	−	0.954664i	$-0.403785\pi$
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	−0.677920	+	0.735135i	$0.737119\pi$
$84$		0			0
$85$	−4.46410	+	0.267949i	−0.484200	+	0.0290632i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	−1.73205	−	1.00000i	−0.184637	−	0.106600i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$	3.46410	+	2.00000i	0.361158	+	0.208514i
$93$		0			0
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$		0			0
$96$		0			0
$97$	6.92820	+	4.00000i	0.703452	+	0.406138i	0.808632	−	0.588315i	$-0.200208\pi$
$97$	6.92820	+	4.00000i	0.703452	+	0.406138i	−0.105180	+	0.994453i	$0.533542\pi$
$98$		−	3.00000i		−	0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$		0			0
$103$	12.1244	−	7.00000i	1.19465	−	0.689730i	0.235291	−	0.971925i	$-0.424396\pi$
$103$	12.1244	−	7.00000i	1.19465	−	0.689730i	0.959357	+	0.282194i	$0.0910623\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−2.46410	−	3.73205i	−0.234943	−	0.355837i
$111$		0			0
$112$	1.73205	−	1.00000i	0.163663	−	0.0944911i
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$114$		0			0
$115$	4.92820	+	7.46410i	0.459557	+	0.696031i
$116$		0			0
$117$		0			0
$118$			10.0000i			0.920575i
$119$	2.00000	−	3.46410i	0.183340	−	0.317554i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.73205	+	1.00000i	−0.156813	+	0.0905357i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.803848	−	13.3923i	−0.0705021	−	1.17458i
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		0			0
$133$		0			0
$134$	−8.00000			−0.691095
$135$		0			0
$136$	−2.00000			−0.171499
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.985577	−	0.169226i	$-0.0541268\pi$
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.346235	+	0.938148i	$0.387460\pi$
$138$		0			0
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	−0.882823	−	0.469706i	$-0.844360\pi$
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	0.0346338	−	0.999400i	$-0.488974\pi$
$140$	4.46410	−	0.267949i	0.377285	−	0.0226458i
$141$		0			0
$142$	10.3923	+	6.00000i	0.872103	+	0.503509i
$143$		−	12.0000i		−	1.00349i
$144$		0			0
$145$		0			0
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$		0			0
$148$	−1.73205	+	1.00000i	−0.142374	+	0.0821995i
$149$	−10.0000	−	17.3205i	−0.819232	−	1.41895i	−0.906249	−	0.422744i	$-0.861067\pi$
$149$	−10.0000	−	17.3205i	−0.819232	−	1.41895i	0.0870170	−	0.996207i	$-0.472267\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$		0			0
$154$	4.00000			0.322329
$155$	−14.9282	+	9.85641i	−1.19906	+	0.791686i
$156$		0			0
$157$	19.0526	−	11.0000i	1.52056	−	0.877896i	0.520854	−	0.853646i	$-0.325614\pi$
$157$	19.0526	−	11.0000i	1.52056	−	0.877896i	0.999706	−	0.0242497i	$-0.00771967\pi$
$158$		0			0
$159$		0			0
$160$	−1.23205	−	1.86603i	−0.0974022	−	0.147522i
$161$	−8.00000			−0.630488
$162$		0			0
$163$		−	16.0000i		−	1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$		−	16.0000i		−	1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	1.00000	−	1.73205i	0.0780869	−	0.135250i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	−0.0407502	−	0.999169i	$-0.512975\pi$
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	0.844931	+	0.534875i	$0.179641\pi$
$168$		0			0
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$	−4.00000	−	2.00000i	−0.306786	−	0.153393i
$171$		0			0
$172$		−	4.00000i		−	0.304997i
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.0375896	−	0.999293i	$-0.511968\pi$
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.884208	+	0.467093i	$0.845301\pi$
$174$		0			0
$175$	9.19615	+	3.92820i	0.695164	+	0.296944i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	8.66025	+	5.00000i	0.649113	+	0.374766i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	10.3923	+	6.00000i	0.770329	+	0.444750i
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−4.46410	+	0.267949i	−0.328207	+	0.0197000i
$186$		0			0
$187$	−3.46410	−	2.00000i	−0.253320	−	0.146254i
$188$			8.00000i			0.583460i
$189$		0			0
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$			22.0000i			1.56744i	0.621117	+	0.783718i	$0.286679\pi$
$197$			22.0000i			1.56744i	−0.621117	+	0.783718i	$0.713321\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−0.598076	−	4.96410i	−0.0422904	−	0.351015i
$201$		0			0
$202$	6.92820	−	4.00000i	0.487467	−	0.281439i
$203$		0			0
$204$		0			0
$205$	3.73205	−	2.46410i	0.260658	−	0.172100i
$206$	14.0000			0.975426
$207$		0			0
$208$		−	6.00000i		−	0.416025i
$209$		0			0
$210$		0			0
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$		0			0
$217$		−	16.0000i		−	1.08615i
$218$	−8.66025	−	5.00000i	−0.586546	−	0.338643i
$219$		0			0
$220$	−0.267949	−	4.46410i	−0.0180651	−	0.300970i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	22.5167	+	13.0000i	1.50783	+	0.870544i	0.999959	+	0.00910984i	$0.00289979\pi$
$223$	22.5167	+	13.0000i	1.50783	+	0.870544i	0.507869	+	0.861435i	$0.330434\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	−6.00000			−0.399114
$227$	24.2487	+	14.0000i	1.60944	+	0.929213i	0.989494	+	0.144571i	$0.0461801\pi$
$227$	24.2487	+	14.0000i	1.60944	+	0.929213i	0.619949	+	0.784642i	$0.287153\pi$
$228$		0			0
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	0.535898	+	8.92820i	0.0353361	+	0.588708i
$231$		0			0
$232$		0			0
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$		0			0
$235$	−8.00000	+	16.0000i	−0.521862	+	1.04372i
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$		0			0
$238$	3.46410	−	2.00000i	0.224544	−	0.129641i
$239$	10.0000	+	17.3205i	0.646846	+	1.12037i	0.983872	+	0.178875i	$0.0572458\pi$
$239$	10.0000	+	17.3205i	0.646846	+	1.12037i	−0.337026	+	0.941495i	$0.609421\pi$
$240$		0			0
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	0.256814	+	0.966461i	$0.417327\pi$
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	−0.965387	+	0.260822i	$0.916006\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	5.59808	−	3.69615i	0.357648	−	0.236139i
$246$		0			0
$247$		0			0
$248$	−6.92820	+	4.00000i	−0.439941	+	0.254000i
$249$		0			0
$250$	3.76795	−	10.5263i	0.238306	−	0.665740i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$			8.00000i			0.502956i
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		0			0
$259$	2.00000	−	3.46410i	0.124274	−	0.215249i
$260$	6.00000	−	12.0000i	0.372104	−	0.744208i
$261$		0			0
$262$			18.0000i			1.11204i
$263$	−3.46410	−	2.00000i	−0.213606	−	0.123325i	0.389380	−	0.921077i	$-0.372689\pi$
$263$	−3.46410	−	2.00000i	−0.213606	−	0.123325i	−0.602986	+	0.797752i	$0.706023\pi$
$264$		0			0
$265$	13.3923	−	0.803848i	0.822683	−	0.0493800i
$266$		0			0
$267$		0			0
$268$	−6.92820	−	4.00000i	−0.423207	−	0.244339i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−1.73205	−	1.00000i	−0.105021	−	0.0606339i
$273$		0			0
$274$	9.00000	+	15.5885i	0.543710	+	0.941733i
$275$	3.92820	−	9.19615i	0.236880	−	0.554549i
$276$		0			0
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$		−	20.0000i		−	1.19952i
$279$		0			0
$280$	4.00000	+	2.00000i	0.239046	+	0.119523i
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$		0			0
$283$	−13.8564	+	8.00000i	−0.823678	+	0.475551i	−0.851683	−	0.524057i	$-0.824418\pi$
$283$	−13.8564	+	8.00000i	−0.823678	+	0.475551i	0.0280052	+	0.999608i	$0.491084\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$			4.00000i			0.236113i
$288$		0			0
$289$	13.0000			0.764706
$290$		0			0
$291$		0			0
$292$	−3.46410	+	2.00000i	−0.202721	+	0.117041i
$293$	−5.19615	+	3.00000i	−0.303562	+	0.175262i	−0.644042	−	0.764990i	$-0.722744\pi$
$293$	−5.19615	+	3.00000i	−0.303562	+	0.175262i	0.340480	+	0.940252i	$0.389411\pi$
$294$		0			0
$295$	−18.6603	+	12.3205i	−1.08644	+	0.717328i
$296$	−2.00000			−0.116248
$297$		0			0
$298$		−	20.0000i		−	1.15857i
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	6.92820	−	4.00000i	0.398673	−	0.230174i
$303$		0			0
$304$		0			0
$305$	−4.00000	−	2.00000i	−0.229039	−	0.114520i
$306$		0			0
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$	3.46410	+	2.00000i	0.197386	+	0.113961i
$309$		0			0
$310$	−17.8564	+	1.07180i	−1.01418	+	0.0608740i
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−3.46410	−	2.00000i	−0.195803	−	0.113047i	0.398894	−	0.916997i	$-0.369394\pi$
$313$	−3.46410	−	2.00000i	−0.195803	−	0.113047i	−0.594696	+	0.803951i	$0.702728\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$		0			0
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	0.450570	−	0.892741i	$-0.351221\pi$
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	−0.547852	+	0.836576i	$0.684554\pi$
$318$		0			0
$319$		0			0
$320$	−0.133975	−	2.23205i	−0.00748941	−	0.124775i
$321$		0			0
$322$	−6.92820	−	4.00000i	−0.386094	−	0.222911i
$323$		0			0
$324$		0			0
$325$	24.0000	−	18.0000i	1.33128	−	0.998460i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	1.73205	−	1.00000i	0.0956365	−	0.0552158i
$329$	−8.00000	−	13.8564i	−0.441054	−	0.763928i
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$		−	4.00000i		−	0.219529i
$333$		0			0
$334$	12.0000			0.656611
$335$	−9.85641	−	14.9282i	−0.538513	−	0.815615i
$336$		0			0
$337$	−24.2487	+	14.0000i	−1.32091	+	0.762629i	−0.983874	−	0.178863i	$-0.942758\pi$
$337$	−24.2487	+	14.0000i	−1.32091	+	0.762629i	−0.337037	+	0.941491i	$0.609425\pi$
$338$	19.9186	−	11.5000i	1.08343	−	0.625518i
$339$		0			0
$340$	−2.46410	−	3.73205i	−0.133635	−	0.202399i
$341$	−16.0000			−0.866449
$342$		0			0
$343$			20.0000i			1.07990i
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$		0			0
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$		0			0
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	6.00000	+	8.00000i	0.320713	+	0.427618i
$351$		0			0
$352$		−	2.00000i		−	0.106600i
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	0.141344	−	0.989960i	$-0.454858\pi$
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	−0.786659	+	0.617388i	$0.788191\pi$
$354$		0			0
$355$	1.60770	+	26.7846i	0.0853276	+	1.42158i
$356$	5.00000	+	8.66025i	0.264999	+	0.458993i
$357$		0			0
$358$	−8.66025	−	5.00000i	−0.457709	−	0.264258i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	1.73205	+	1.00000i	0.0910346	+	0.0525588i
$363$		0			0
$364$	6.00000	+	10.3923i	0.314485	+	0.544705i
$365$	−8.92820	+	0.535898i	−0.467324	+	0.0280502i
$366$		0			0
$367$	−1.73205	−	1.00000i	−0.0904123	−	0.0521996i	0.454112	−	0.890945i	$-0.349957\pi$
$367$	−1.73205	−	1.00000i	−0.0904123	−	0.0521996i	−0.544524	+	0.838745i	$0.683290\pi$
$368$			4.00000i			0.208514i
$369$		0			0
$370$	−4.00000	−	2.00000i	−0.207950	−	0.103975i
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$		0			0
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	−0.628454	−	0.777847i	$-0.716312\pi$
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	0.359408	+	0.933181i	$0.382979\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$		0			0
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$	−10.3923	+	6.00000i	−0.531717	+	0.306987i
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	−0.810331	−	0.585973i	$-0.800713\pi$
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	0.102302	+	0.994753i	$0.467379\pi$
$384$		0			0
$385$	4.92820	+	7.46410i	0.251164	+	0.380406i
$386$	4.00000			0.203595
$387$		0			0
$388$			8.00000i			0.406138i
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	−0.492947	−	0.870059i	$-0.664080\pi$
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	0.999967	−	0.00812520i	$-0.00258636\pi$
$390$		0			0
$391$	4.00000	+	6.92820i	0.202289	+	0.350374i
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$		0			0
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$		0			0
$396$		0			0
$397$			2.00000i			0.100377i	0.998740	+	0.0501886i	$0.0159822\pi$
$397$			2.00000i			0.100377i	−0.998740	+	0.0501886i	$0.984018\pi$
$398$		0			0
$399$		0			0
$400$	1.96410	−	4.59808i	0.0982051	−	0.229904i
$401$	−11.0000	−	19.0526i	−0.549314	−	0.951439i	−0.998322	−	0.0579116i	$-0.981556\pi$
$401$	−11.0000	−	19.0526i	−0.549314	−	0.951439i	0.449008	−	0.893528i	$-0.351777\pi$
$402$		0			0
$403$	−41.5692	−	24.0000i	−2.07071	−	1.19553i
$404$	8.00000			0.398015
$405$		0			0
$406$		0			0
$407$	−3.46410	−	2.00000i	−0.171709	−	0.0991363i
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	4.46410	−	0.267949i	0.220466	−	0.0132331i
$411$		0			0
$412$	12.1244	+	7.00000i	0.597324	+	0.344865i
$413$		−	20.0000i		−	0.984136i
$414$		0			0
$415$	4.00000	−	8.00000i	0.196352	−	0.392705i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$		0			0
$418$		0			0
$419$	−5.00000	−	8.66025i	−0.244266	−	0.423081i	0.717659	−	0.696395i	$-0.245214\pi$
$419$	−5.00000	−	8.66025i	−0.244266	−	0.423081i	−0.961925	+	0.273314i	$0.911880\pi$
$420$		0			0
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	0.463002	+	0.886357i	$0.346772\pi$
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$		−	12.0000i		−	0.584151i
$423$		0			0
$424$	6.00000			0.291386
$425$	−1.19615	−	9.92820i	−0.0580219	−	0.481589i
$426$		0			0
$427$	3.46410	−	2.00000i	0.167640	−	0.0967868i
$428$	−10.3923	+	6.00000i	−0.502331	+	0.290021i
$429$		0			0
$430$	7.46410	−	4.92820i	0.359951	−	0.237659i
$431$	32.0000			1.54139			0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000			1.54139			0.770693	+	0.637207i	$0.219910\pi$
$432$		0			0
$433$			4.00000i			0.192228i	0.995370	+	0.0961139i	$0.0306413\pi$
$433$			4.00000i			0.192228i	−0.995370	+	0.0961139i	$0.969359\pi$
$434$	8.00000	−	13.8564i	0.384012	−	0.665129i
$435$		0			0
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$		0			0
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	2.00000	−	4.00000i	0.0953463	−	0.190693i
$441$		0			0
$442$		−	12.0000i		−	0.570782i
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$		0			0
$445$	1.33975	+	22.3205i	0.0635100	+	1.05809i
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$		0			0
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$		0			0
$454$	14.0000	+	24.2487i	0.657053	+	1.13805i
$455$	1.60770	+	26.7846i	0.0753699	+	1.25568i
$456$		0			0
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.316579	−	0.948566i	$-0.602534\pi$
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.979772	+	0.200118i	$0.935868\pi$
$458$		−	10.0000i		−	0.467269i
$459$		0			0
$460$	−4.00000	+	8.00000i	−0.186501	+	0.373002i
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	−0.971248	−	0.238071i	$-0.923485\pi$
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	0.691800	+	0.722089i	$0.256818\pi$
$462$		0			0
$463$	−5.19615	+	3.00000i	−0.241486	+	0.139422i	−0.615859	−	0.787856i	$-0.711191\pi$
$463$	−5.19615	+	3.00000i	−0.241486	+	0.139422i	0.374374	+	0.927278i	$0.377858\pi$
$464$		0			0
$465$		0			0
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$	−14.9282	+	9.85641i	−0.688587	+	0.454642i
$471$		0			0
$472$	−8.66025	+	5.00000i	−0.398621	+	0.230144i
$473$	6.92820	−	4.00000i	0.318559	−	0.183920i
$474$		0			0
$475$		0			0
$476$	4.00000			0.183340
$477$		0			0
$478$			20.0000i			0.914779i
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	−0.541884	−	0.840453i	$-0.682289\pi$
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	0.998796	+	0.0490589i	$0.0156222\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−19.0526	+	11.0000i	−0.867820	+	0.501036i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−8.00000	+	16.0000i	−0.363261	+	0.726523i
$486$		0			0
$487$		−	18.0000i		−	0.815658i	−0.913058	−	0.407829i	$-0.866286\pi$
$487$		−	18.0000i		−	0.815658i	0.913058	−	0.407829i	$-0.133714\pi$
$488$	−1.73205	−	1.00000i	−0.0784063	−	0.0452679i
$489$		0			0
$490$	6.69615	−	0.401924i	0.302501	−	0.0181571i
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	0.994456	−	0.105151i	$-0.0335327\pi$
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	−0.588292	+	0.808649i	$0.700199\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	8.52628	−	7.23205i	0.381307	−	0.323427i
$501$		0			0
$502$	−15.5885	−	9.00000i	−0.695747	−	0.401690i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$		0			0
$508$	−1.73205	+	1.00000i	−0.0768473	+	0.0443678i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−18.0000			−0.793946
$515$	17.2487	+	26.1244i	0.760069	+	1.15118i
$516$		0			0
$517$	−13.8564	+	8.00000i	−0.609404	+	0.351840i
$518$	3.46410	−	2.00000i	0.152204	−	0.0878750i
$519$		0			0
$520$	11.1962	−	7.39230i	0.490984	−	0.324174i
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$		−	16.0000i		−	0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$		−	16.0000i		−	0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	−9.00000	+	15.5885i	−0.393167	+	0.680985i
$525$		0			0
$526$	−2.00000	−	3.46410i	−0.0872041	−	0.151042i
$527$	−13.8564	+	8.00000i	−0.603595	+	0.348485i
$528$		0			0
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$	12.0000	+	6.00000i	0.521247	+	0.260623i
$531$		0			0
$532$		0			0
$533$	10.3923	+	6.00000i	0.450141	+	0.259889i
$534$		0			0
$535$	−26.7846	+	1.60770i	−1.15800	+	0.0695067i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$		0			0
$538$		0			0
$539$	6.00000			0.258438
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$	−6.92820	−	4.00000i	−0.297592	−	0.171815i
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	−1.33975	−	22.3205i	−0.0573884	−	0.956106i
$546$		0			0
$547$	24.2487	+	14.0000i	1.03680	+	0.598597i	0.918925	−	0.394432i	$-0.129059\pi$
$547$	24.2487	+	14.0000i	1.03680	+	0.598597i	0.117875	+	0.993028i	$0.462392\pi$
$548$			18.0000i			0.768922i
$549$		0			0
$550$	8.00000	−	6.00000i	0.341121	−	0.255841i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$	2.46410	+	3.73205i	0.104127	+	0.157708i
$561$		0			0
$562$	15.5885	−	9.00000i	0.657559	−	0.379642i
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.615673	−	0.788002i	$-0.288884\pi$
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.990266	−	0.139188i	$-0.0444492\pi$
$564$		0			0
$565$	−7.39230	−	11.1962i	−0.310997	−	0.471026i
$566$	−16.0000			−0.672530
$567$		0			0
$568$			12.0000i			0.503509i
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$	10.3923	−	6.00000i	0.434524	−	0.250873i
$573$		0			0
$574$	−2.00000	+	3.46410i	−0.0834784	+	0.144589i
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$		0			0
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$		0			0
$580$		0			0
$581$	4.00000	+	6.92820i	0.165948	+	0.287430i
$582$		0			0
$583$	10.3923	+	6.00000i	0.430405	+	0.248495i
$584$	−4.00000			−0.165521
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−10.3923	−	6.00000i	−0.428936	−	0.247647i	0.269957	−	0.962872i	$-0.412990\pi$
$587$	−10.3923	−	6.00000i	−0.428936	−	0.247647i	−0.698893	+	0.715226i	$0.746324\pi$
$588$		0			0
$589$		0			0
$590$	−22.3205	+	1.33975i	−0.918921	+	0.0551565i
$591$		0			0
$592$	−1.73205	−	1.00000i	−0.0711868	−	0.0410997i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$		0			0
$595$	8.00000	+	4.00000i	0.327968	+	0.163984i
$596$	10.0000	−	17.3205i	0.409616	−	0.709476i
$597$		0			0
$598$	−20.7846	+	12.0000i	−0.849946	+	0.490716i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	−0.885700	−	0.464258i	$-0.846321\pi$
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	0.844909	+	0.534910i	$0.179654\pi$
$602$			8.00000i			0.326056i
$603$		0			0
$604$	8.00000			0.325515
$605$	−13.0622	+	8.62436i	−0.531053	+	0.350630i
$606$		0			0
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	−0.0607380	−	0.998154i	$-0.519345\pi$
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	0.834058	+	0.551678i	$0.186012\pi$
$608$		0			0
$609$		0			0
$610$	−2.46410	−	3.73205i	−0.0997686	−	0.151106i
$611$	−48.0000			−1.94187
$612$		0			0
$613$		−	26.0000i		−	1.05013i	−0.851062	−	0.525065i	$-0.824041\pi$
$613$		−	26.0000i		−	1.05013i	0.851062	−	0.525065i	$-0.175959\pi$
$614$	−6.00000	+	10.3923i	−0.242140	+	0.419399i
$615$		0			0
$616$	2.00000	+	3.46410i	0.0805823	+	0.139573i
$617$	1.73205	−	1.00000i	0.0697297	−	0.0402585i	−0.464730	−	0.885453i	$-0.653849\pi$
$617$	1.73205	−	1.00000i	0.0697297	−	0.0402585i	0.534460	+	0.845194i	$0.320515\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$	−16.0000	−	8.00000i	−0.642575	−	0.321288i
$621$		0			0
$622$		−	12.0000i		−	0.481156i
$623$	−17.3205	−	10.0000i	−0.693932	−	0.400642i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−2.00000	−	3.46410i	−0.0799361	−	0.138453i
$627$		0			0
$628$	19.0526	+	11.0000i	0.760280	+	0.438948i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$		0			0
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−4.46410	+	0.267949i	−0.177152	+	0.0106332i
$636$		0			0
$637$	15.5885	+	9.00000i	0.617637	+	0.356593i
$638$		0			0
$639$		0			0
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		0			0
$643$	20.7846	−	12.0000i	0.819665	−	0.473234i	−0.0306359	−	0.999531i	$-0.509753\pi$
$643$	20.7846	−	12.0000i	0.819665	−	0.473234i	0.850301	+	0.526297i	$0.176420\pi$
$644$	−4.00000	−	6.92820i	−0.157622	−	0.273009i
$645$		0			0
$646$		0			0
$647$		−	48.0000i		−	1.88707i	−0.331266	−	0.943537i	$-0.607476\pi$
$647$		−	48.0000i		−	1.88707i	0.331266	−	0.943537i	$-0.392524\pi$
$648$		0			0
$649$	−20.0000			−0.785069
$650$	29.7846	−	3.58846i	1.16825	−	0.140751i
$651$		0			0
$652$	13.8564	−	8.00000i	0.542659	−	0.313304i
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.871036	−	0.491220i	$-0.836551\pi$
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.0101092	+	0.999949i	$0.503218\pi$
$654$		0			0
$655$	−33.5885	+	22.1769i	−1.31241	+	0.866524i
$656$	2.00000			0.0780869
$657$		0			0
$658$		−	16.0000i		−	0.623745i
$659$	−25.0000	+	43.3013i	−0.973862	+	1.68678i	−0.290220	+	0.956960i	$0.593729\pi$
$659$	−25.0000	+	43.3013i	−0.973862	+	1.68678i	−0.683641	+	0.729818i	$0.739605\pi$
$660$		0			0
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	0.845922	−	0.533306i	$-0.179051\pi$
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	−0.884818	+	0.465937i	$0.845717\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$		0			0
$664$	2.00000	−	3.46410i	0.0776151	−	0.134433i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	10.3923	+	6.00000i	0.402090	+	0.232147i
$669$		0			0
$670$	−1.07180	−	17.8564i	−0.0414071	−	0.689853i
$671$	−2.00000	−	3.46410i	−0.0772091	−	0.133730i
$672$		0			0
$673$	31.1769	+	18.0000i	1.20178	+	0.693849i	0.960951	−	0.276718i	$-0.0892468\pi$
$673$	31.1769	+	18.0000i	1.20178	+	0.693849i	0.240831	+	0.970567i	$0.422580\pi$
$674$	−28.0000			−1.07852
$675$		0			0
$676$	23.0000			0.884615
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	0.466347	−	0.884602i	$-0.345570\pi$
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	−0.532915	+	0.846169i	$0.678903\pi$
$678$		0			0
$679$	−8.00000	−	13.8564i	−0.307012	−	0.531760i
$680$	−0.267949	−	4.46410i	−0.0102754	−	0.171190i
$681$		0			0
$682$	−13.8564	−	8.00000i	−0.530589	−	0.306336i
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	−18.0000	+	36.0000i	−0.687745	+	1.37549i
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$		0			0
$688$	3.46410	−	2.00000i	0.132068	−	0.0762493i
$689$	18.0000	+	31.1769i	0.685745	+	1.18775i
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	12.0000			0.455514
$695$	37.3205	−	24.6410i	1.41565	−	0.934687i
$696$		0			0
$697$	3.46410	−	2.00000i	0.131212	−	0.0757554i
$698$	8.66025	−	5.00000i	0.327795	−	0.189253i
$699$		0			0
$700$	1.19615	+	9.92820i	0.0452103	+	0.375251i
$701$	32.0000			1.20862			0.604312	−	0.796748i	$-0.293448\pi$
$701$	32.0000			1.20862			0.604312	+	0.796748i	$0.293448\pi$
$702$		0			0
$703$		0			0
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$		0			0
$706$	−7.00000	−	12.1244i	−0.263448	−	0.456306i
$707$	−13.8564	+	8.00000i	−0.521124	+	0.300871i
$708$		0			0
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	−0.433865	−	0.900978i	$-0.642851\pi$
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	0.997202	−	0.0747503i	$-0.0238160\pi$
$710$	−12.0000	+	24.0000i	−0.450352	+	0.900704i
$711$		0			0
$712$			10.0000i			0.374766i
$713$	27.7128	+	16.0000i	1.03785	+	0.599205i
$714$		0			0
$715$	26.7846	−	1.60770i	1.00169	−	0.0601244i
$716$	−5.00000	−	8.66025i	−0.186859	−	0.323649i
$717$		0			0
$718$		0			0
$719$	40.0000			1.49175			0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000			1.49175			0.745874	+	0.666087i	$0.232032\pi$
$720$		0			0
$721$	−28.0000			−1.04277
$722$	−16.4545	−	9.50000i	−0.612372	−	0.353553i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$	15.5885	+	9.00000i	0.578144	+	0.333792i	0.760395	−	0.649460i	$-0.225005\pi$
$727$	15.5885	+	9.00000i	0.578144	+	0.333792i	−0.182252	+	0.983252i	$0.558339\pi$
$728$			12.0000i			0.444750i
$729$		0			0
$730$	−8.00000	−	4.00000i	−0.296093	−	0.148047i
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	12.1244	−	7.00000i	0.447823	−	0.258551i	−0.259087	−	0.965854i	$-0.583422\pi$
$733$	12.1244	−	7.00000i	0.447823	−	0.258551i	0.706910	+	0.707303i	$0.250088\pi$
$734$	−1.00000	−	1.73205i	−0.0369107	−	0.0639312i
$735$		0			0
$736$	−2.00000	+	3.46410i	−0.0737210	+	0.127688i
$737$		−	16.0000i		−	0.589368i
$738$		0			0
$739$	−40.0000			−1.47142			−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000			−1.47142			−0.735712	+	0.677295i	$0.763152\pi$
$740$	−2.46410	−	3.73205i	−0.0905822	−	0.137193i
$741$		0			0
$742$	−10.3923	+	6.00000i	−0.381514	+	0.220267i
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	−0.0676840	−	0.997707i	$-0.521561\pi$
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	0.830197	+	0.557470i	$0.188228\pi$
$744$		0			0
$745$	37.3205	−	24.6410i	1.36732	−	0.902777i
$746$	−6.00000			−0.219676
$747$		0			0
$748$		−	4.00000i		−	0.146254i
$749$	12.0000	−	20.7846i	0.438470	−	0.759453i
$750$		0			0
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	−6.92820	+	4.00000i	−0.252646	+	0.145865i
$753$		0			0
$754$		0			0
$755$	16.0000	+	8.00000i	0.582300	+	0.291150i
$756$		0			0
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	−17.3205	−	10.0000i	−0.629109	−	0.363216i
$759$		0			0
$760$		0			0
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$		0			0
$763$	17.3205	+	10.0000i	0.627044	+	0.362024i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−16.0000			−0.578103
$767$	−51.9615	−	30.0000i	−1.87622	−	1.08324i
$768$		0			0
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	−0.998852	−	0.0479061i	$-0.984745\pi$
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	0.457938	−	0.888984i	$-0.348588\pi$
$770$	0.535898	+	8.92820i	0.0193124	+	0.321750i
$771$		0			0
$772$	3.46410	+	2.00000i	0.124676	+	0.0719816i
$773$			54.0000i			1.94225i	0.238581	+	0.971123i	$0.423318\pi$
$773$			54.0000i			1.94225i	−0.238581	+	0.971123i	$0.576682\pi$
$774$		0			0
$775$	−24.0000	−	32.0000i	−0.862105	−	1.14947i
$776$	−4.00000	+	6.92820i	−0.143592	+	0.248708i
$777$		0			0
$778$	17.3205	−	10.0000i	0.620970	−	0.358517i
$779$		0			0
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$			8.00000i			0.286079i
$783$		0			0
$784$	3.00000			0.107143
$785$	27.1051	+	41.0526i	0.967423	+	1.46523i
$786$		0			0
$787$	27.7128	−	16.0000i	0.987855	−	0.570338i	0.0832226	−	0.996531i	$-0.473479\pi$
$787$	27.7128	−	16.0000i	0.987855	−	0.570338i	0.904632	+	0.426193i	$0.140145\pi$
$788$	−19.0526	+	11.0000i	−0.678719	+	0.391859i
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$		−	12.0000i		−	0.426132i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$		0			0
$797$	1.73205	−	1.00000i	0.0613524	−	0.0354218i	−0.469010	−	0.883193i	$-0.655389\pi$
$797$	1.73205	−	1.00000i	0.0613524	−	0.0354218i	0.530362	+	0.847771i	$0.322056\pi$
$798$		0			0
$799$	−8.00000	+	13.8564i	−0.283020	+	0.490204i
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$		0			0
$802$		−	22.0000i		−	0.776847i
$803$	−6.92820	−	4.00000i	−0.244491	−	0.141157i
$804$		0			0
$805$	−1.07180	−	17.8564i	−0.0377759	−	0.629356i
$806$	−24.0000	−	41.5692i	−0.845364	−	1.46421i
$807$		0			0
$808$	6.92820	+	4.00000i	0.243733	+	0.140720i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$		0			0
$813$		0			0
$814$	−2.00000	−	3.46410i	−0.0701000	−	0.121417i
$815$	35.7128	−	2.14359i	1.25097	−	0.0750868i
$816$		0			0
$817$		0			0
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$	4.00000	+	2.00000i	0.139686	+	0.0698430i
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	−0.787745	−	0.616002i	$-0.788751\pi$
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	0.927346	+	0.374206i	$0.122085\pi$
$822$		0			0
$823$	−5.19615	+	3.00000i	−0.181126	+	0.104573i	−0.587822	−	0.808990i	$-0.700014\pi$
$823$	−5.19615	+	3.00000i	−0.181126	+	0.104573i	0.406695	+	0.913564i	$0.366681\pi$
$824$	7.00000	+	12.1244i	0.243857	+	0.422372i
$825$		0			0
$826$	10.0000	−	17.3205i	0.347945	−	0.602658i
$827$		−	28.0000i		−	0.973655i	−0.873498	−	0.486828i	$-0.838154\pi$
$827$		−	28.0000i		−	0.973655i	0.873498	−	0.486828i	$-0.161846\pi$
$828$		0			0
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$	7.46410	−	4.92820i	0.259083	−	0.171060i
$831$		0			0
$832$	5.19615	−	3.00000i	0.180144	−	0.104006i
$833$	5.19615	−	3.00000i	0.180036	−	0.103944i
$834$		0			0
$835$	14.7846	+	22.3923i	0.511643	+	0.774918i
$836$		0			0
$837$		0			0
$838$		−	10.0000i		−	0.345444i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−19.0526	+	11.0000i	−0.656595	+	0.379085i
$843$		0			0
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	46.0000	+	23.0000i	1.58245	+	0.791224i
$846$		0			0
$847$		−	14.0000i		−	0.481046i
$848$	5.19615	+	3.00000i	0.178437	+	0.103020i
$849$		0			0
$850$	3.92820	−	9.19615i	0.134736	−	0.315425i
$851$	4.00000	+	6.92820i	0.137118	+	0.237496i
$852$		0			0
$853$	−12.1244	−	7.00000i	−0.415130	−	0.239675i	0.277862	−	0.960621i	$-0.410374\pi$
$853$	−12.1244	−	7.00000i	−0.415130	−	0.239675i	−0.692992	+	0.720946i	$0.743708\pi$
$854$	4.00000			0.136877
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.272882	−	0.962048i	$-0.587977\pi$
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.969599	+	0.244701i	$0.921310\pi$
$858$		0			0
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	8.92820	−	0.535898i	0.304449	−	0.0182740i
$861$		0			0
$862$	27.7128	+	16.0000i	0.943902	+	0.544962i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$		0			0
$865$	14.0000	−	28.0000i	0.476014	−	0.952029i
$866$	−2.00000	+	3.46410i	−0.0679628	+	0.117715i
$867$		0			0
$868$	13.8564	−	8.00000i	0.470317	−	0.271538i
$869$		0			0
$870$		0			0
$871$	24.0000	−	41.5692i	0.813209	−	1.40852i
$872$		−	10.0000i		−	0.338643i
$873$		0			0
$874$		0			0
$875$	−7.53590	+	21.0526i	−0.254760	+	0.711706i
$876$		0			0
$877$	19.0526	−	11.0000i	0.643359	−	0.371444i	−0.142548	−	0.989788i	$-0.545530\pi$
$877$	19.0526	−	11.0000i	0.643359	−	0.371444i	0.785907	+	0.618344i	$0.212196\pi$
$878$		0			0
$879$		0			0
$880$	3.73205	−	2.46410i	0.125807	−	0.0830648i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$			24.0000i			0.807664i	0.914833	+	0.403832i	$0.132322\pi$
$883$			24.0000i			0.807664i	−0.914833	+	0.403832i	$0.867678\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	−0.315279	−	0.948999i	$-0.602098\pi$
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	0.664218	+	0.747539i	$0.268765\pi$
$888$		0			0
$889$	2.00000	−	3.46410i	0.0670778	−	0.116182i
$890$	−10.0000	+	20.0000i	−0.335201	+	0.670402i
$891$		0			0
$892$			26.0000i			0.870544i
$893$		0			0
$894$		0			0
$895$	−1.33975	−	22.3205i	−0.0447828	−	0.746092i
$896$	1.00000	+	1.73205i	0.0334077	+	0.0578638i
$897$		0			0
$898$	−25.9808	−	15.0000i	−0.866989	−	0.500556i
$899$		0			0
$900$		0			0
$901$	12.0000			0.399778
$902$	3.46410	+	2.00000i	0.115342	+	0.0665927i
$903$		0			0
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	0.267949	+	4.46410i	0.00890693	+	0.148392i
$906$		0			0
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	0.317441	−	0.948278i	$-0.397176\pi$
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	−0.662512	+	0.749051i	$0.730510\pi$
$908$			28.0000i			0.929213i
$909$		0			0
$910$	−12.0000	+	24.0000i	−0.397796	+	0.795592i
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	−0.127585	−	0.991828i	$-0.540723\pi$
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	0.922740	−	0.385422i	$-0.125944\pi$
$912$		0			0
$913$	6.92820	−	4.00000i	0.229290	−	0.132381i
$914$	−16.0000	−	27.7128i	−0.529233	−	0.916658i
$915$		0			0
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$		−	36.0000i		−	1.18882i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−7.46410	+	4.92820i	−0.246084	+	0.162478i
$921$		0			0
$922$	−10.3923	+	6.00000i	−0.342252	+	0.197599i
$923$	−62.3538	+	36.0000i	−2.05240	+	1.18495i
$924$		0			0
$925$	−1.19615	−	9.92820i	−0.0393292	−	0.326437i
$926$	−6.00000			−0.197172
$927$		0			0
$928$		0			0
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$		0			0
$931$		0			0
$932$	−12.1244	+	7.00000i	−0.397146	+	0.229293i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	4.00000	−	8.00000i	0.130814	−	0.261628i
$936$		0			0
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$	13.8564	+	8.00000i	0.452428	+	0.261209i
$939$		0			0
$940$	−17.8564	+	1.07180i	−0.582412	+	0.0349582i
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	0.998767	−	0.0496480i	$-0.0158099\pi$
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	−0.542380	+	0.840133i	$0.682477\pi$
$942$		0			0
$943$	−6.92820	−	4.00000i	−0.225613	−	0.130258i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	8.00000			0.260102
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$		0			0
$952$	3.46410	+	2.00000i	0.112272	+	0.0648204i
$953$		−	46.0000i		−	1.49009i	−0.667016	−	0.745043i	$-0.732429\pi$
$953$		−	46.0000i		−	1.49009i	0.667016	−	0.745043i	$-0.267571\pi$
$954$		0			0
$955$	−24.0000	−	12.0000i	−0.776622	−	0.388311i
$956$	−10.0000	+	17.3205i	−0.323423	+	0.560185i
$957$		0			0
$958$	17.3205	−	10.0000i	0.559600	−	0.323085i
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		−	12.0000i		−	0.386896i
$963$		0			0
$964$	−22.0000			−0.708572
$965$	4.92820	+	7.46410i	0.158644	+	0.240278i
$966$		0			0
$967$	−32.9090	+	19.0000i	−1.05828	+	0.610999i	−0.924956	−	0.380074i	$-0.875899\pi$
$967$	−32.9090	+	19.0000i	−1.05828	+	0.610999i	−0.133325	+	0.991072i	$0.542565\pi$
$968$	−6.06218	+	3.50000i	−0.194846	+	0.112494i
$969$		0			0
$970$	−14.9282	+	9.85641i	−0.479316	+	0.316470i
$971$	−18.0000			−0.577647			−0.288824	−	0.957382i	$-0.593264\pi$
$971$	−18.0000			−0.577647			−0.288824	+	0.957382i	$0.593264\pi$
$972$		0			0
$973$			40.0000i			1.28234i
$974$	9.00000	−	15.5885i	0.288379	−	0.499486i
$975$		0			0
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.211495	−	0.977379i	$-0.432167\pi$
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.952183	+	0.305530i	$0.0988335\pi$
$978$		0			0
$979$	−10.0000	+	17.3205i	−0.319601	+	0.553566i
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$		0			0
$982$			18.0000i			0.574403i
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	0.704425	−	0.709779i	$-0.251205\pi$
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	−0.262474	+	0.964939i	$0.584538\pi$
$984$		0			0
$985$	−49.1051	+	2.94744i	−1.56462	+	0.0939133i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.0000			−0.508770
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−6.92820	−	4.00000i	−0.219971	−	0.127000i
$993$		0			0
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$		0			0
$996$		0			0
$997$	15.5885	+	9.00000i	0.493691	+	0.285033i	0.726105	−	0.687584i	$-0.241329\pi$
$997$	15.5885	+	9.00000i	0.493691	+	0.285033i	−0.232413	+	0.972617i	$0.574662\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.i.e.379.2		4
3.2	odd	2		810.2.i.b.379.1		4
5.4	even	2	inner	810.2.i.e.379.1		4
9.2	odd	6		90.2.c.a.19.2		2
9.4	even	3	inner	810.2.i.e.109.1		4
9.5	odd	6		810.2.i.b.109.2		4
9.7	even	3		30.2.c.a.19.1	✓	2
15.14	odd	2		810.2.i.b.379.2		4
36.7	odd	6		240.2.f.a.49.1		2
36.11	even	6		720.2.f.f.289.2		2
45.2	even	12		450.2.a.b.1.1		1
45.4	even	6	inner	810.2.i.e.109.2		4
45.7	odd	12		150.2.a.c.1.1		1
45.14	odd	6		810.2.i.b.109.1		4
45.29	odd	6		90.2.c.a.19.1		2
45.34	even	6		30.2.c.a.19.2	yes	2
45.38	even	12		450.2.a.f.1.1		1
45.43	odd	12		150.2.a.a.1.1		1
63.16	even	3		1470.2.n.h.949.1		4
63.25	even	3		1470.2.n.h.79.2		4
63.34	odd	6		1470.2.g.g.589.1		2
63.52	odd	6		1470.2.n.a.79.2		4
63.61	odd	6		1470.2.n.a.949.1		4
72.11	even	6		2880.2.f.c.1729.1		2
72.29	odd	6		2880.2.f.e.1729.1		2
72.43	odd	6		960.2.f.i.769.2		2
72.61	even	6		960.2.f.h.769.1		2
144.43	odd	12		3840.2.d.j.2689.1		2
144.61	even	12		3840.2.d.g.2689.2		2
144.115	odd	12		3840.2.d.x.2689.2		2
144.133	even	12		3840.2.d.y.2689.1		2
180.7	even	12		1200.2.a.g.1.1		1
180.43	even	12		1200.2.a.m.1.1		1
180.47	odd	12		3600.2.a.bg.1.1		1
180.79	odd	6		240.2.f.a.49.2		2
180.83	odd	12		3600.2.a.o.1.1		1
180.119	even	6		720.2.f.f.289.1		2
315.34	odd	6		1470.2.g.g.589.2		2
315.79	even	6		1470.2.n.h.949.2		4
315.97	even	12		7350.2.a.cc.1.1		1
315.124	odd	6		1470.2.n.a.949.2		4
315.214	even	6		1470.2.n.h.79.1		4
315.223	even	12		7350.2.a.bg.1.1		1
315.304	odd	6		1470.2.n.a.79.1		4
360.29	odd	6		2880.2.f.e.1729.2		2
360.43	even	12		4800.2.a.m.1.1		1
360.133	odd	12		4800.2.a.cg.1.1		1
360.187	even	12		4800.2.a.cj.1.1		1
360.259	odd	6		960.2.f.i.769.1		2
360.277	odd	12		4800.2.a.l.1.1		1
360.299	even	6		2880.2.f.c.1729.2		2
360.349	even	6		960.2.f.h.769.2		2
720.259	odd	12		3840.2.d.j.2689.2		2
720.349	even	12		3840.2.d.y.2689.2		2
720.619	odd	12		3840.2.d.x.2689.1		2
720.709	even	12		3840.2.d.g.2689.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.c.a.19.1	✓	2	9.7	even	3
30.2.c.a.19.2	yes	2	45.34	even	6
90.2.c.a.19.1		2	45.29	odd	6
90.2.c.a.19.2		2	9.2	odd	6
150.2.a.a.1.1		1	45.43	odd	12
150.2.a.c.1.1		1	45.7	odd	12
240.2.f.a.49.1		2	36.7	odd	6
240.2.f.a.49.2		2	180.79	odd	6
450.2.a.b.1.1		1	45.2	even	12
450.2.a.f.1.1		1	45.38	even	12
720.2.f.f.289.1		2	180.119	even	6
720.2.f.f.289.2		2	36.11	even	6
810.2.i.b.109.1		4	45.14	odd	6
810.2.i.b.109.2		4	9.5	odd	6
810.2.i.b.379.1		4	3.2	odd	2
810.2.i.b.379.2		4	15.14	odd	2
810.2.i.e.109.1		4	9.4	even	3	inner
810.2.i.e.109.2		4	45.4	even	6	inner
810.2.i.e.379.1		4	5.4	even	2	inner
810.2.i.e.379.2		4	1.1	even	1	trivial
960.2.f.h.769.1		2	72.61	even	6
960.2.f.h.769.2		2	360.349	even	6
960.2.f.i.769.1		2	360.259	odd	6
960.2.f.i.769.2		2	72.43	odd	6
1200.2.a.g.1.1		1	180.7	even	12
1200.2.a.m.1.1		1	180.43	even	12
1470.2.g.g.589.1		2	63.34	odd	6
1470.2.g.g.589.2		2	315.34	odd	6
1470.2.n.a.79.1		4	315.304	odd	6
1470.2.n.a.79.2		4	63.52	odd	6
1470.2.n.a.949.1		4	63.61	odd	6
1470.2.n.a.949.2		4	315.124	odd	6
1470.2.n.h.79.1		4	315.214	even	6
1470.2.n.h.79.2		4	63.25	even	3
1470.2.n.h.949.1		4	63.16	even	3
1470.2.n.h.949.2		4	315.79	even	6
2880.2.f.c.1729.1		2	72.11	even	6
2880.2.f.c.1729.2		2	360.299	even	6
2880.2.f.e.1729.1		2	72.29	odd	6
2880.2.f.e.1729.2		2	360.29	odd	6
3600.2.a.o.1.1		1	180.83	odd	12
3600.2.a.bg.1.1		1	180.47	odd	12
3840.2.d.g.2689.1		2	720.709	even	12
3840.2.d.g.2689.2		2	144.61	even	12
3840.2.d.j.2689.1		2	144.43	odd	12
3840.2.d.j.2689.2		2	720.259	odd	12
3840.2.d.x.2689.1		2	720.619	odd	12
3840.2.d.x.2689.2		2	144.115	odd	12
3840.2.d.y.2689.1		2	144.133	even	12
3840.2.d.y.2689.2		2	720.349	even	12
4800.2.a.l.1.1		1	360.277	odd	12
4800.2.a.m.1.1		1	360.43	even	12
4800.2.a.cg.1.1		1	360.133	odd	12
4800.2.a.cj.1.1		1	360.187	even	12
7350.2.a.bg.1.1		1	315.223	even	12
7350.2.a.cc.1.1		1	315.97	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-5.19615 + 3.00000i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.00000i q^{17} +(-1.86603 + 1.23205i) q^{20} +(-1.73205 + 1.00000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -6.00000 q^{26} -2.00000i q^{28} +(4.00000 + 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(2.00000 - 4.00000i) q^{35} +2.00000i q^{37} +(-2.23205 + 0.133975i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(-3.46410 - 2.00000i) q^{43} -2.00000 q^{44} +4.00000 q^{46} +(6.92820 + 4.00000i) q^{47} +(-1.50000 - 2.59808i) q^{49} +(-4.59808 - 1.96410i) q^{50} +(-5.19615 - 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 - 2.00000i) q^{55} +(1.00000 - 1.73205i) q^{56} +(5.00000 + 8.66025i) q^{59} +(-1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-7.39230 - 11.1962i) q^{65} +(-6.92820 + 4.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(3.73205 - 2.46410i) q^{70} +12.0000 q^{71} +4.00000i q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.46410 - 2.00000i) q^{77} +(-2.00000 - 1.00000i) q^{80} -2.00000i q^{82} +(-3.46410 - 2.00000i) q^{83} +(-4.46410 + 0.267949i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.73205 - 1.00000i) q^{88} +10.0000 q^{89} +12.0000 q^{91} +(3.46410 + 2.00000i) q^{92} +(4.00000 + 6.92820i) q^{94} +(6.92820 + 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5	\( 4 q + 2 q^{4} + 4 q^{5} - 4 q^{10} - 4 q^{11} - 4 q^{14} - 2 q^{16} - 4 q^{20} - 6 q^{25} - 24 q^{26} + 16 q^{31} - 4 q^{34} + 8 q^{35} - 2 q^{40} - 4 q^{41} - 8 q^{44} + 16 q^{46} - 6 q^{49} - 8 q^{50} - 16 q^{55} + 4 q^{56} + 20 q^{59} - 4 q^{61} - 4 q^{64} + 12 q^{65} + 8 q^{70} + 48 q^{71} - 4 q^{74} - 8 q^{80} - 4 q^{85} - 8 q^{86} + 40 q^{89} + 48 q^{91} + 16 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 - 4 * q^10 - 4 * q^11 - 4 * q^14 - 2 * q^16 - 4 * q^20 - 6 * q^25 - 24 * q^26 + 16 * q^31 - 4 * q^34 + 8 * q^35 - 2 * q^40 - 4 * q^41 - 8 * q^44 + 16 * q^46 - 6 * q^49 - 8 * q^50 - 16 * q^55 + 4 * q^56 + 20 * q^59 - 4 * q^61 - 4 * q^64 + 12 * q^65 + 8 * q^70 + 48 * q^71 - 4 * q^74 - 8 * q^80 - 4 * q^85 - 8 * q^86 + 40 * q^89 + 48 * q^91 + 16 * q^94

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